Mimicking general relativity in the Solar System

In order for a modified gravity model to be a candidate for cosmological dark energy, it has to pass stringent local gravity experiments. We find that a Brans-Dicke (BD) theory with well-defined second order corrections that include the Gauss-Bonnet term possesses this feature. We construct the generic second order theory that gives, to linear order, a BD metric solution for a pointlike mass source. We find that the Eddington parameter γ, heavily constrained by time delay experiments, can be arbitrarily close to the general relativity value of 1, with an arbitrary BD parameter ωBD. We find the region where the solution is stable to small timelike perturbations.